Mawla of Asma, Abdullah, narrates that Sayyida Asma (may Allah be pleased with her) was staying near the place where people were staying. She used to ask: "Young son! Has the moon set?" This was the night of Muzdalifah and she was praying. I said: "No." Then she prayed for a while and asked: "Son! Has the moon set?" At that time, the moon had set. I said: "Yes." Upon hearing this, she said: "Let us go." So we set out and went and performed the stoning of Jamrat al-Aqabah. After that, she returned and performed the Fajr prayer at her place. I said: "Respected lady, we have done this very early." She replied: "Son! Not at all. The Prophet of Allah gave permission for weak women to do so."
Hadith Takhrij«أخرجه البخاري: 1679، ومسلم: 1291، (انظر مسند أحمد ترقيم الرسالة: 26941 ترقیم بيت الأفكار الدولية: 27480»
Brief Explanation
Benefits: … (10) According to the date, the moon sets a little while after approximately two-thirds of the night has passed. However, in hadith number (4500), it is mentioned that the Messenger of Allah (sallallahu alayhi wa sallam) granted permission to certain people to leave Muzdalifah at night, and also instructed them that they should perform the stoning (rami) after sunrise. See the answer to this in the benefits of the referenced hadith.